Update(Response to questions about example; with 'infelicity' and 'solecism' adopted from an answer)

Inaccurate -- The sentence (from a sci.math newsgroup posting by "AP") is inaccurate or misleading in first using the "multiplication of ..." infelicity one way for the (10^10)^60 calculation, and then a different way for the (10^600)*(10^3) calculation. That is, if the first case means (10^10)^60, the second might be thought to mean either (10^10)^(10^3) or (10^600)^(10^3).

Clumsy -- The solecisms "a multiplication of 60 of the 10^10 terms to get us to 10^600" and "a multiplication of 10^3 terms to reach 10^603" are longwinded and ambiguous ways to say "compute 10^600 as the 60th power of 10^10" and "compute 10^603 as (10^600)*(10^3)".

I am not sure that your example is 'clumsy, inaccurate and ambiguous'. Assuming there is at least a some context in which this sentence exists it might not be inaccurate nor ambiguous at all. Can you give more examples?
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UnreasonOct 18 '11 at 8:04

@Unreason Yesterday I overlooked your request for more examples, but rather than more examples have today added some details about the current one. Thanks!
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jwpat7Oct 19 '11 at 4:49

5 Answers
5

solecism |ˈsäləˌsizəm, ˈsō-|noun
a grammatical mistake in speech or writing.

or possibly

malaprop |ˈmaləˌpräp|(also malapropism )noun
the mistaken use of a word in place of a similar-sounding one, often with unintentionally amusing effect, as in, for example, “dance a flamingo ” (instead of flamenco).

or perhaps my personal favorite

infelicity |ɪnfɪˈlɪsɪti|noun ( pl. infelicities )
1 a thing that is inappropriate, especially a remark or expression: she winced at their infelicities and at the clumsy way they talked.

Although the answer is educational, OP is not looking for stylistic vices that add to 'clumsiness, inaccuracy and ambiguity'. Also note that solecism only deals with grammatical mistake that OP did not ask for. A more complete list of stylistic vices can be found here: rhetoric.byu.edu/Figures/Groupings/Vices.htm and most of them (except possibly the ones that deal with repetition) are related to the question in the same way malapropism is.
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UnreasonOct 18 '11 at 8:40

@Unreason: These are not "stylistic vices that add to 'clumsiness, inaccuracy, and ambiguity,'" they are instances of maladroitness of speech or writing, and hence constitute "a word or phrase useful for referring to a bad sentence ..." as the OP sets forth in the first sentence of the question.
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RobustoOct 18 '11 at 12:56

Pending the clarification of your question here's a brief exposition of mechanisms that might be at play here:

You ask for a single term that describes 'clumsiness, inaccuracy and ambiguity', however usually such erroneous properties are classified into two categories: stylistic vices and (logical) fallacies.

Ambiguity as fallacy is well defined here (and I feel it might cover inaccuracy as well).

Clumsiness on the other hand is a very vague term which can be aided by any number of stylistic vices, listed here.

Single term might be possible, but you will have to be more precise or be satisfied with general terms such as 'muddled' that you propose yourself.
If this is the course that you want to take, which might not be more judgmental than the more exact classifications presented above, but is definitively harder to argue for, you should look at synonyms of

1 The antonyms of 'clumsy' are more subjective as it might be expected, since 'clumsy' itself is essentially less objective than the terms 'ambiguous' and 'inaccurate'. You might want to ignore them if you are striving not to be perceived as judgmental.

Also, do look at the synonyms of synonyms, too. There is a myriad of terms that might apply, depending on what you actually need.

Though abstruse is a fine word, it is defined as 1. difficult to understand, which might not be due to badly written text, but due to complexity (and OP needs to clarify the question, I find his example simply a bit complex and it might not be ambiguous)
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UnreasonOct 18 '11 at 9:31

@Unreason (and rems) While 'abstruse' does mean difficult to comprehend or understand, it does not denote (nor, I think, connote) incorrect or clumsy. [On another note, I see that 'recondite' has a sense synonymous with abstruse; but 'recondite' also has a sense unwelcome in present case: "Of a person: highly talented, a master of a field".]
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jwpat7Oct 19 '11 at 5:07

@rems You are right that the example sentence is confusingly and a little incoherently written. 'Incoherent' is stronger and 'confusing' is weaker than I wanted; however, I ended up using a fairly weak term anyway ('misleading') in a response.
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jwpat7Oct 19 '11 at 5:18